Modeling and Analysis on AC-DC Harmonic Coupling of the Three-Phase Voltage Source Converter under Asymmetric Condition
Abstract
:1. Introduction
2. Harmonic State Space Method
3. HSS Modeling for the Three-Phase VSC Topology under Asymmetric Conditions
3.1. Average State Space Model of the Three-Phase VSC
3.2. HSS Modeling of the Three-Phase VSC
4. HSS Modeling of the VSC Control System under Asymmetric Conditions
4.1. T/4 Delay Link
4.2. DDSRF Current Loop
4.3. DC-Link Voltage/Reactive Power Loop
4.4. HSS Model of the VSC Controller
5. HSS Small-Signal Modeling
- (1)
- There is strong coupling between the AC-side positive and negative sequences and the DC-side current harmonics. For the nΔth-order harmonic current on the DC side, the coupled AC-side positive- and negative-sequence currents are both of (nΔ ± k)th-order (k = 1, 3, 5, …).
- (2)
- In general, the non-zero elements of the harmonic coupling matrix decrease with the increase of nΔ and k. That is, in the figure, the amplitudes of the elements on both adjacent positions along the main diagonal are the largest, while the amplitudes decay from left to right. In addition, the amplitudes of elements far from the main diagonal are lower;
- (3)
- In symmetric cases without the T/4-delay link [7], along the main diagonal direction, the matrix elements decrease monotonically. However, with the influence of the positive and negative sequence separation links based on T/4 delay, the AC-DC inter-harmonic coupling relationship near the fundamental frequency is significantly weakened. This conclusion is supported by both Figure 5a,b, where the amplitudes of elements (2, 1) and (1, 2) are smaller than those of adjacent elements;
- (4)
- When modeling other asymmetric working conditions and outer loop control strategies, it is only necessary to modify ucqt according to the positive and negative sequence voltage conditions of the AC port in a specific scenario. In the meantime, it just needs to modify uctrl3 and the correlation coefficient matrix Bctrl3 and Dctrl3 according to the specific control strategy. Therefore, the modeling method proposed in this paper exhibits good generality and extensibility.
6. Simulation Verification and Discussion
7. Conclusions
- (1)
- The proposed modeling method provides a practical solution to the steady-state modeling problem of the T/4-delay-based DDSRF control system, which highlights the accurate steady-state characteristics description without increasing the model complexity. In addition, the proposed modeling method has good versatility and ductility, which can be easily extended to different symmetrical working conditions.
- (2)
- Strong coupling exists between the positive- and negative-sequence current harmonics and the DC current harmonics. For the nΔth-order harmonic current on the DC side, the coupled AC-side positive- and negative-sequence currents are both of (nΔ ± k)th-order (k = 1, 3, 5, …).
- (3)
- The T/4-delay-based sequence-separation link has considerable influence on the coupling relationship, i.e., compared with existing research results that utilize other separation techniques, the AC-DC inter-harmonic coupling near the fundamental frequency is significantly attenuated.
- (4)
- The output of the established model shows good matching performance with the electromagnetic transient simulation, indicating that it can correctly reflect the steady-state harmonic coupling characteristics of the three-phase VSC.
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
References
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Parameter | Value [Unit] |
---|---|
AC side rated voltage | 10 [kV] |
AC side asymmetry condition | Current of Phase A dropped to 0.1 p.u. |
AC side control strategy | Suppression of negative sequence current |
DC side input power | 10 [MW] |
AC side output power command | 10 [MMW], 1 [Mvar] |
DC link rated voltage | 20 [kV] |
AC side filter inductor | 10 [mH] |
AC side equivalent resistance | 0.1 [Ω] |
DC link capacitor value | 100 [μF] |
PWM carrier frequency | 10 [kHz] |
PI gain of voltage outer loop | (0.1, 10) |
PI gain of reactive outer loop | (0.01, 1) |
PI gain of current inner loop | (5, 100) |
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Wu, W.; Li, J.; Mao, T.; Liu, S.; Zhou, B.; Zeng, D. Modeling and Analysis on AC-DC Harmonic Coupling of the Three-Phase Voltage Source Converter under Asymmetric Condition. Energies 2022, 15, 5466. https://doi.org/10.3390/en15155466
Wu W, Li J, Mao T, Liu S, Zhou B, Zeng D. Modeling and Analysis on AC-DC Harmonic Coupling of the Three-Phase Voltage Source Converter under Asymmetric Condition. Energies. 2022; 15(15):5466. https://doi.org/10.3390/en15155466
Chicago/Turabian StyleWu, Wei, Jing Li, Tian Mao, Shenquan Liu, Baorong Zhou, and Dehui Zeng. 2022. "Modeling and Analysis on AC-DC Harmonic Coupling of the Three-Phase Voltage Source Converter under Asymmetric Condition" Energies 15, no. 15: 5466. https://doi.org/10.3390/en15155466
APA StyleWu, W., Li, J., Mao, T., Liu, S., Zhou, B., & Zeng, D. (2022). Modeling and Analysis on AC-DC Harmonic Coupling of the Three-Phase Voltage Source Converter under Asymmetric Condition. Energies, 15(15), 5466. https://doi.org/10.3390/en15155466